Finite Group Databasebeta

← C2×#19143753 #25961697

Subgroups — C2×#19143753 #25961697

Order 11008.

1982 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583427C211yesmaximal, characteristic
2#19143753C2116yesmaximal, direct product factor
3C2×#14583028C211yesmaximal, characteristic, complemented
4C2×#14583023C211yesmaximal, characteristic, complemented
5C2×#14582975C211yesmaximal, characteristic, complemented
6C2×#14582969C211yesmaximal, characteristic, complemented
7C2×#14582968C211yesmaximal, characteristic, complemented
8C2×#14582964C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
11C2×#14582960C211yesmaximal, characteristic, complemented
12C2×#14582959C211yesmaximal, characteristic, complemented
13C2×#14582951C211yesmaximal, characteristic, complemented
14C2×#14582924C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#424C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583427C418yes—
22#14583427C2218yes—
23C2×#13063320C411yescharacteristic
24C2×#13063318C411yescharacteristic
25C2×#13063315C411yescharacteristic
26C2×#13063311C411yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063307C411yescharacteristic
29C2×#13063303C411yescharacteristic
30C2×#13063298C411yescharacteristic
31C2×C4×Dic86C2211yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36C2×C42×D43C2211yescharacteristic
37#14583028C2218yescomplemented
38#14583023C2218yescomplemented
39#14582975C2218yescomplemented
40#14582969C2218yescomplemented
41#14582968C2218yescomplemented
42#14582964C2218yescomplemented
43C8×C22⋊D43C2218yescomplemented
44C8×C22⋊D43C2218yescomplemented
45#14582960C2218yescomplemented
46#14582959C2218yescomplemented
47#14582951C2218yescomplemented
48#14582924C2218yescomplemented
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C2×Dic43⋊C8C2211yescharacteristic
52C2×Dic43⋊C8C2211yescharacteristic
53C2×Dic43⋊C8C2211yescharacteristic
54C2×Dic43⋊C8C2211yescharacteristic
55C4⋊C8×D43C2218yescomplemented
56C2×C22⋊(C43⋊C8)C2211yescharacteristic
57C2×C22⋊(C43⋊C8)C2211yescharacteristic
58C2×(C2×D43)⋊C8C2211yescharacteristic
59C2×(C2×D43)⋊C8C2211yescharacteristic
60C2×(C2×D43)⋊C8C2211yescharacteristic
61C2×(C2×D43)⋊C8C2211yescharacteristic
62C2×#13063236C2211yescharacteristic
63C2×#13063235C2211yescharacteristic
64C2×C4×C43⋊C8C2211yescharacteristic
65C2×C8×Dic43C2211yescharacteristic
66C2×C8×Dic43C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C22×M16×C43C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#424C2218yescomplemented
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×C4⋊C8×C43C2211yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621872—42no—
85C2×#10621872C2314yes—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C2×C8×D43—42no—
91C2×C8×D43—42no—
92C2×C8×D43—42no—
93C2×C8×D43C2314yes—
94C2×C8×D43C2314yes—
95C2×C8×D43C2314yes—
96#13063320C2×C418yes—
97#13063318C2×C418yes—
98#13063315C2×C418yes—
99#13063311C2×C418yes—
100#13063310C2×C418yes—
101#13063307C2×C418yes—
102#13063303C2×C418yes—
103#13063298C2×C418yes—
104C4×Dic86C2×C414yes—
105C4×Dic86C2314yes—
106C4×D172C2×C414yes—
107C4×D172C2314yes—
108C4×C22⋊D43C2×C414yes—
109C4×C22⋊D43C2×C414yes—
110C4×C22⋊D43C2314yes—
111C4×C22⋊D43C2314yes—
112#13063282C2×C414yes—
113#13063282C2314yes—
114C2×C4⋊Dic43C2×C411yescharacteristic
115C2×C4⋊Dic43C2×C411yescharacteristic
116C2×Dic43⋊C4C2×C411yescharacteristic
117C2×Dic43⋊C4C2×C411yescharacteristic
118C2×Dic43⋊C4C2×C411yescharacteristic
119C2×Dic43⋊C4C2×C411yescharacteristic
120C2×Dic43⋊C4C2×C411yescharacteristic
121C2×Dic43⋊C4C2×C411yescharacteristic
122C2×C22⋊Dic43C2×C411yescharacteristic
123C2×C22⋊Dic43C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C2×(C2×D43)⋊C4C2×C411yescharacteristic
127C2×(C2×D43)⋊C4C2×C411yescharacteristic
128C2×(C2×D43)⋊C4C2×C411yescharacteristic
129C2×(C2×D43)⋊C4C2×C411yescharacteristic
130C2×C4×Dic43C2×C411yescharacteristic
131C2×C4×Dic43C2×C411yescharacteristic
132C2×C4×Dic43C2311yescharacteristic
133C2×C4×Dic43C2311yescharacteristic
134C42×D43C2×C414yes—
135C42×D43C2314yes—
136C4⋊(C43⋊C8)C2314yes—
137C4⋊(C43⋊C8)C2314yes—
138Dic43⋊C8C2314yes—
139Dic43⋊C8C2314yes—
140Dic43⋊C8C2314yes—
141Dic43⋊C8C2314yes—
142C22⋊(C43⋊C8)C2314yes—
143C22⋊(C43⋊C8)C2314yes—
144(C2×D43)⋊C8C2314yes—
145(C2×D43)⋊C8C2314yes—
146(C2×D43)⋊C8C2314yes—
147(C2×D43)⋊C8C2314yes—
148#13063236C2314yes—
149#13063235C2314yes—
150C4×C43⋊C8C2314yes—
151C8×Dic43C2314yes—
152C8×Dic43C2314yes—
153C8×Dic43C2314yes—
154C23×C4×C43C2311yescharacteristic
155C2×M16×C43—42no—
156C2×M16×C43C2314yes—
157C22×C8×C43—42no—
158C22×C8×C43C2311yescharacteristic
159C22×C8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2314yes—
163#117×C43C2×C414yes—
164#117×C43C2314yes—
165C2×C4⋊C4×C43C2×C411yescharacteristic
166C2×C4⋊C4×C43C2×C411yescharacteristic
167C2×C22⋊C4×C43C2×C411yescharacteristic
168C2×C22⋊C4×C43C2×C411yescharacteristic
169C2×C42×C43C2311yescharacteristic
170C2×C42×C43C2311yescharacteristic
171C4⋊C8×C43C2314yes—
172C4⋊C8×C43C2314yes—
173C4⋊C8×C43C2314yes—
174C4⋊C8×C43C2314yes—
175C24×C43C22×C411yescharacteristic
176C23×D43C22×C411yescharacteristic
177C23×D43C22×C411yescharacteristic
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C22×C411yescharacteristic
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C22×C412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—24no—
189C2×C22⋊D43—24no—
190C2×C22⋊D43C22×C414yes—
191C2×C22⋊D43C22×C414yes—
192C22×Dic43C22×C411yescharacteristic
193C22×Dic43C22×C411yescharacteristic
194C22×Dic43C22×C411yescharacteristic
195C22×Dic43C22×C411yescharacteristic
196C22×Dic43C22×C411yescharacteristic
197C22×Dic43C22×C411yescharacteristic
198C2×D172—24no—
199C2×D172C22×C414yes—
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—22no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43C22×C412yes—
207C2×C4×D43C22×C414yes—
208C2×C4×D43C22×C414yes—
209C2×C4×D43C22×C412yes—
210C2×C4×D43C2412yes—
211C2×C4×D43C2412yes—
212C2×Dic86—24no—
213C2×Dic86C22×C414yes—
214M16×C43—44no—
215C2×C8×C43—22no—
216C2×C8×C43—22no—
217C2×C8×C43—22no—
218C2×C8×C43—22no—
219C2×C8×C43—44no—
220C2×C8×C43C2412yes—
221C2×C8×C43C2412yes—
222C2×C8×C43C2412yes—
223C2×C8×C43C2412yes—
224C4⋊C4×C43C22×C414yes—
225C4⋊C4×C43C22×C414yes—
226C22⋊C4×C43C22×C414yes—
227C22⋊C4×C43C22×C414yes—
228C42×C43C22×C412yes—
229C42×C43C22×C412yes—
230C42×C43C2412yes—
231C42×C43C2412yes—
232C22⋊Dic43C22×C414yes—
233C22⋊Dic43C22×C414yes—
234(C2×D43)⋊C4C22×C414yes—
235(C2×D43)⋊C4C22×C414yes—
236(C2×D43)⋊C4C22×C414yes—
237(C2×D43)⋊C4C22×C414yes—
238(C2×D43)⋊C4C22×C414yes—
239(C2×D43)⋊C4C22×C414yes—
240C4⋊Dic43C22×C414yes—
241C4⋊Dic43C22×C414yes—
242Dic43⋊C4C22×C414yes—
243Dic43⋊C4C22×C414yes—
244Dic43⋊C4C22×C414yes—
245Dic43⋊C4C22×C414yes—
246Dic43⋊C4C22×C414yes—
247Dic43⋊C4C22×C414yes—
248C4×Dic43C22×C412yes—
249C4×Dic43C22×C414yes—
250C4×Dic43C22×C414yes—
251C4×Dic43C22×C412yes—
252C4×Dic43C2412yes—
253C4×Dic43C2412yes—
254C2×C43⋊C8—22no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8C2412yes—
259C2×C43⋊C8C2412yes—
260C2×C43⋊C8C2412yes—
261C2×C43⋊C8C2412yes—
262#10621872—44no—
263C8×D43—44no—
264C8×D43—44no—
265C8×D43—44no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43C23×C412yes—
270C23×C43C23×C411yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43#13114yes—
277C22×D43C23×C412yes—
278C22×D43C23×C412yes—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—24no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43C23×C412yes—
288C2×C4×C43C23×C412yes—
289C2×C4×C43C23×C412yes—
290C2×C4×C43C23×C412yes—
291C2×C4×C43C23×C412yes—
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43H(5,𝔽2)12yes—
294C2×C4×C432−1+412yes—
295C2×C4×C43C2511yescharacteristic
296C22⋊D43—28no—
297C22⋊D43—28no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43#13114yes—
304C2×Dic43C23×C412yes—
305C2×Dic43C23×C412yes—
306C2×Dic43C23×C412yes—
307C2×Dic43C23×C412yes—
308C2×Dic43C23×C412yes—
309C2×Dic43C23×C412yes—
310D172—28no—
311C4×D43—28no—
312C4×D43—24no—
313C4×D43—24no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—28no—
319Dic86—28no—
320C8×C43—22no—
321C8×C43—22no—
322C8×C43—22no—
323C8×C43—22no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C2×#2994—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—44no—
333C22×C43#52012yes—
334C22×C43C2×#13112yes—
335C22×C43C2×#13112yes—
336C22×C43C24×C411yescharacteristic
337C2×D43—22no—
338C2×D43—28no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—44no—
344C2×D43C2×#13114yes—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43#52012yes—
351C4×C43C2×H(5,𝔽2)11yescharacteristic
352C4×C43C2×2−1+411yescharacteristic
353Dic43—22no—
354Dic43—22no—
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43C2×#13114yes—
359C2×#529—431no—
360#2994—4316no—
361C2×#446—431no—
362C2×C8×Q8—431no—
363C2×#436—431no—
364C2×#435—431no—
365C2×#435—431no—
366C2×C8×D4—431no—
367C2×C8×D4—431no—
368C2×C8×D4—431no—
369C2×#433—431no—
370C2×#433—431no—
371C2×#431—431no—
372C2×#424—431no—
373C2×#424D4311yescharacteristic, complemented
374C22×C4⋊C8—431no—
375C2×C43—42no—
376C2×C43#299414yescomplemented
377C2×C43C2×#52011yescharacteristic
378C2×C43C22×#13111yescharacteristic
379C2×C43C22×#13111yescharacteristic
380D43—24no—
381D43—42no—
382C22×M16—431no—
383C22×M16C2×D4311yescharacteristic
384C23×C8—431no—
385C23×C8—431no—
386C23×C8—431no—
387C23×C8C2×D4311yescharacteristic
388#529—438no—
389#529—438no—
390C2×#126—431no—
391C2×#126—431no—
392C2×#125—431no—
393C2×#124—431no—
394C2×#123—431no—
395C2×#123—431no—
396C2×C22⋊Q8—431no—
397C2×#121—431no—
398C2×C4×Q8—431no—
399C2×C4×D4—431no—
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×#117—431no—
403C2×#117C2×D4311yescharacteristic
404C22×C42—431no—
405#446—438no—
406C8×Q8—438no—
407#436—438no—
408#435—438no—
409#435—438no—
410C8×D4—438no—
411C8×D4—438no—
412C8×D4—438no—
413#433—438no—
414#433—438no—
415#431—438no—
416#424—438no—
417#424C2×D4318yescomplemented
418C2×C4⋊C8—431no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—431no—
421C2×C4⋊C8—431no—
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8—438no—
425C2×C4⋊C8C2×D4311yescharacteristic
426C2×C4⋊C8C2×D4311yescharacteristic
427C2×C4⋊C8C2×D4311yescharacteristic
428C2×C4⋊C8C2×D4311yescharacteristic
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×#97—431no—
436C2×#97—431no—
437C2×C4×C8—431no—
438C2×C4×C8—431no—
439C2×C4×C8—431no—
440C2×C4×C8—431no—
441C43C2×#299411yescharacteristic, complemented, Sylow
442C22×Q8—431no—
443C22×D4—431no—
444C22×D4—431no—
445C22×D4—431no—
446C23×C4—431no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4C22×D4311yescharacteristic
451C2×M16—42no—
452C2×M16—434no—
453C2×M16—1722no—
454C2×M16C22×D4314yes—
455C22×C8—42no—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—434no—
461C22×C8—434no—
462C22×C8—434no—
463C22×C8—1722no—
464C22×C8—1722no—
465C22×C8—1722no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4314yes—
471#126—438no—
472#126—438no—
473#125—438no—
474#124—438no—
475#123—438no—
476#123—438no—
477C22⋊Q8—438no—
478#121—438no—
479C4×Q8—434no—
480C4×Q8—434no—
481C4×D4—434no—
482C4×D4—434no—
483C4×D4—434no—
484C4×D4—434no—
485C4×D4—434no—
486C4×D4—434no—
487#117—434no—
488#117—434no—
489#117C4×D4314yes—
490#117C22×D4314yes—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4C4×D4311yescharacteristic
500C2×C4⋊C4C4×D4311yescharacteristic
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4C4×D4311yescharacteristic
510C2×C22⋊C4C4×D4311yescharacteristic
511C2×C42—431no—
512C2×C42—431no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—434no—
516C2×C42—434no—
517C2×C42C22×D4311yescharacteristic
518C2×C42C22×D4311yescharacteristic
519C4⋊C8—434no—
520C4⋊C8—434no—
521C4⋊C8—434no—
522C4⋊C8—434no—
523C4⋊C8—434no—
524C4⋊C8—434no—
525C4⋊C8C22×D4314yes—
526C4⋊C8C22×D4314yes—
527C4⋊C8C22×D4314yes—
528C4⋊C8C22×D4314yes—
529C22⋊C8—434no—
530C22⋊C8—434no—
531C22⋊C8—434no—
532C22⋊C8—434no—
533C22⋊C8—434no—
534C22⋊C8—434no—
535#97—434no—
536#97—434no—
537C4×C8—434no—
538C4×C8—434no—
539C4×C8—434no—
540C4×C8—434no—
541C24—431no—
542C24—431no—
543C24C2×C4×D4311yescharacteristic
544C2×Q8—434no—
545C2×Q8—864no—
546C2×D4—434no—
547C2×D4—434no—
548C2×D4—434no—
549C2×D4—864no—
550C2×D4—864no—
551C2×D4—864no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—432no—
561C22×C4—434no—
562C22×C4—434no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—864no—
567C22×C4—864no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4C2×C4×D4311yescharacteristic
573C22×C4C2×C4×D4311yescharacteristic
574C22×C4C2×C4×D4311yescharacteristic
575C22×C4C2×C4×D4311yescharacteristic
576C22×C4C2×C4×D4311yescharacteristic
577C22×C4C2×C4×D4312yes—
578C22×C4C23×D4312yes—
579C22×C4C23×D4311yescharacteristic
580M16—44no—
581M16—1724no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—44no—
587C2×C8—432no—
588C2×C8—432no—
589C2×C8—432no—
590C2×C8—432no—
591C2×C8—862no—
592C2×C8—862no—
593C2×C8—862no—
594C2×C8—862no—
595C2×C8—1724no—
596C2×C8—1724no—
597C2×C8—1724no—
598C2×C8C23×D4312yes—
599C2×C8C23×D4312yes—
600C2×C8C23×D4312yes—
601C2×C8C23×D4312yes—
602C4⋊C4—434no—
603C4⋊C4—434no—
604C4⋊C4—434no—
605C4⋊C4—434no—
606C4⋊C4—434no—
607C4⋊C4—434no—
608C4⋊C4—434no—
609C4⋊C4—434no—
610C4⋊C4C2×C4×D4314yes—
611C4⋊C4C2×C4×D4314yes—
612C22⋊C4—434no—
613C22⋊C4—434no—
614C22⋊C4—434no—
615C22⋊C4—434no—
616C22⋊C4—434no—
617C22⋊C4—434no—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4C2×C4×D4314yes—
621C22⋊C4C2×C4×D4314yes—
622C42—432no—
623C42—434no—
624C42—434no—
625C42—432no—
626C42—432no—
627C42—432no—
628C42C2×C4×D4312yes—
629C42C2×C4×D4312yes—
630C42C23×D4312yes—
631C42C23×D4312yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—434no—
636C23—432no—
637C23—432no—
638C23—862no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—862no—
643C23C22×C4×D4312yes—
644C23C22×C4×D4311yescharacteristic
645Q8—868no—
646D4—868no—
647D4—868no—
648D4—868no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—434no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—432no—
664C2×C4—868no—
665C2×C4—868no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—864no—
672C2×C4—864no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4C22×C4×D4312yes—
678C2×C4C22×C4×D4312yes—
679C2×C4C22×C4×D4312yes—
680C2×C4C22×C4×D4312yes—
681C2×C4C22×C4×D4312yes—
682C2×C4C22×C4×D4311yescharacteristic
683C2×C4#1306337012yes—
684C2×C4#1306337312yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—862no—
691C8—862no—
692C8—862no—
693C8—862no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—434no—
699C22—862no—
700C22—868no—
701C22—862no—
702C22—862no—
703C22—862no—
704C22—862no—
705C22—1724no—
706C22#1458338012yes—
707C22#131×D4312yes—
708C22#131×D4312yes—
709C22C23×C4×D4311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—434no—
716C4—862no—
717C4—862no—
718C4—862no—
719C4—862no—
720C4—862no—
721C4#1458338012yes—
722C4C2×#1306337011yescharacteristic
723C4C2×#1306337311yescharacteristic
724C2—42no—
725C2—864no—
726C2—1722no—
727C2#1914375314yesdirect product factor
728C2C2×#1458338011yescharacteristic
729C2C2×#131×D4311yescharacteristic
730C2C2×#131×D4311yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#424C2
socleC23×C43C23×C4
prime radicalC2×#13063298C4
cosocleC2×C4×C43C25
hypercenterC2×#424D43
hypocenterC43C2×#2994
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19143753C2direct (N × H)
3. C2×#14583028C2semidirect
4. C2×#14583023C2semidirect
5. C2×#14582975C2semidirect
6. C2×#14582969C2semidirect
7. C2×#14582968C2semidirect
8. C2×#14582964C2semidirect
9. C2×C8×C22⋊D43C2semidirect
10. C2×C8×C22⋊D43C2semidirect
11. C2×#14582960C2semidirect
12. C2×#14582959C2semidirect
13. C2×#14582951C2semidirect
14. C2×#14582924C2semidirect
15. C2×C4⋊C8×D43C2semidirect
16. C2×C43×#424C2semidirect
37. #14583028C22semidirect
38. #14583023C22semidirect
39. #14582975C22semidirect
40. #14582969C22semidirect
41. #14582968C22semidirect
42. #14582964C22semidirect
43. C8×C22⋊D43C22semidirect
44. C8×C22⋊D43C22semidirect
45. #14582960C22semidirect
46. #14582959C22semidirect
47. #14582951C22semidirect
48. #14582924C22semidirect
55. C4⋊C8×D43C22semidirect
71. C43×#424C22semidirect
373. C2×#424D43semidirect
376. C2×C43#2994semidirect
417. #424C2×D43semidirect
441. C43C2×#2994semidirect
727. C2#19143753direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145834272
#191437532
C2×#145830282
C2×#145830232
C2×#145829752
C2×#145829692
C2×#145829682
C2×#145829642
C2×C8×C22⋊D432
C2×#145829602
C2×#145829592
C2×#145829512
C2×#145829242
C2×C4⋊C8×D432
C2×C43×#4242
C2×#299443